Toeplitz operators on bounded symmetric domains

Harald Upmeier
1983 Transactions of the American Mathematical Society  
In this paper Jordan algebraic methods are applied to study Toeplitz operators on the Hardy space H2(S) associated with the Shilov boundary 5 of a bounded symmetric domain D in C" of arbitrary rank. The Jordan triple system Z « C" associated with D is used to determine the relationship between Toeplitz operators and differential operators. Further, it is shown that each Jordan triple idempotent e £ Z induces an irreducible representation ("e-symbol") of the C*algebra \T generated by all
more » ... ated by all Toeplitz operators 7} with continuous symbol function/.
doi:10.1090/s0002-9947-1983-0712257-2 fatcat:6reifkkrsvcq7n7oauncdezw7i